Shakita Huerta
MAT 330 Final Exam
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
dy
=2 y
1 dx
• First Order Linear Equation
•
dy
=2
• y dx
1
dy=2 dx
• y
• ln y=2 x+ c1
• y=e2 x +c
1
• y=e2 x e c 1
• y=ce 2 x
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
dy
x + y=xsin(x)
2 dx
• First Order Linear Equation
• dy
dx
+ (x )
1
y=sin x
∫( 1 )dx
• I . F=e x
• e
ln x
• ¿x
• y (I . F )= ∫ ( I . F) dx+ c
• yx= ∫ xsin(x) dx+ c
This study source was downloaded by 100000847097152 from CourseHero.com on 08-30-2023 15:01:12 GMT -05:00
https://www.coursehero.com/file/31038910/Shakita-Huerta-Final-Exam-330-docx/
, • yx=x (−cos ( x ) )− ∫ (−cosx ) dx +c
• yx=−xcos ( x )+sin ( x ) +c
sin ( x ) c
• y= −cos ( x )+
x x
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
x2 dy
3 x3
3. , y (0 )=2
y −1 dx
2 y
=
• First Order Linear Equation
y
(dy )=3 x
• dx y2−1
y
∫ (dy )=∫ 3 x dx
• y≥ 1
loge y 2− )❑ 3 x
2
• 1
+c
(2 1 = 2
loge y 2− x
2
•
( 1 )
+c
2
2
=
3 x2
1 /2
• ( y −1 ) =K e 2
2
2
• y 2=1+k e 3 x
1/2
• General Solutio n= y=( 1+ k e3 x )
2
• y (0)=2
• (1+k ∙ e0) =2
1/ 2
• (1+k )=4
• k =3
• y (x )= ( 1+3 e3 x 1) 2
2
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
4. y2 dx+ ( 3+ 2 xy ) dy=0
This study source was downloaded by 100000847097152 from CourseHero.com on 08-30-2023 15:01:12 GMT -05:00
https://www.coursehero.com/file/31038910/Shakita-Huerta-Final-Exam-330-docx/
MAT 330 Final Exam
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
dy
=2 y
1 dx
• First Order Linear Equation
•
dy
=2
• y dx
1
dy=2 dx
• y
• ln y=2 x+ c1
• y=e2 x +c
1
• y=e2 x e c 1
• y=ce 2 x
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
dy
x + y=xsin(x)
2 dx
• First Order Linear Equation
• dy
dx
+ (x )
1
y=sin x
∫( 1 )dx
• I . F=e x
• e
ln x
• ¿x
• y (I . F )= ∫ ( I . F) dx+ c
• yx= ∫ xsin(x) dx+ c
This study source was downloaded by 100000847097152 from CourseHero.com on 08-30-2023 15:01:12 GMT -05:00
https://www.coursehero.com/file/31038910/Shakita-Huerta-Final-Exam-330-docx/
, • yx=x (−cos ( x ) )− ∫ (−cosx ) dx +c
• yx=−xcos ( x )+sin ( x ) +c
sin ( x ) c
• y= −cos ( x )+
x x
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
x2 dy
3 x3
3. , y (0 )=2
y −1 dx
2 y
=
• First Order Linear Equation
y
(dy )=3 x
• dx y2−1
y
∫ (dy )=∫ 3 x dx
• y≥ 1
loge y 2− )❑ 3 x
2
• 1
+c
(2 1 = 2
loge y 2− x
2
•
( 1 )
+c
2
2
=
3 x2
1 /2
• ( y −1 ) =K e 2
2
2
• y 2=1+k e 3 x
1/2
• General Solutio n= y=( 1+ k e3 x )
2
• y (0)=2
• (1+k ∙ e0) =2
1/ 2
• (1+k )=4
• k =3
• y (x )= ( 1+3 e3 x 1) 2
2
For the below ordinary differential equation, state the order and determine if
the equation is linear or nonlinear. Then find the general solution of the
ordinary differential equation. Verify your solution.
4. y2 dx+ ( 3+ 2 xy ) dy=0
This study source was downloaded by 100000847097152 from CourseHero.com on 08-30-2023 15:01:12 GMT -05:00
https://www.coursehero.com/file/31038910/Shakita-Huerta-Final-Exam-330-docx/
